Hinge Vertices Research Articles

Evolution of Cooperation for Multiple Mutant Configurations on All Regular Graphs with N ≤ 14 Players

We study the emergence of cooperation in structured populations with any arrangement of cooperators and defectors on the evolutionary graph. In a computational approach using structure coefficients defined for configurations describing such arrangements of any number of mutants, we provide results for weak selection to favor cooperation over defection on any regular graph with N ≤ 14 vertices. Furthermore, the properties of graphs that particularly promote cooperation are analyzed. It is shown that the number of graph cycles of a certain length is a good predictor for the values of the structure coefficient, and thus a tendency to favor cooperation. Another property of particularly cooperation-promoting regular graphs with a low degree is that they are structured to have blocks with clusters of mutants that are connected by cut vertices and/or hinge vertices.

Reciprocal Control of Hierarchical DNA Origami-Nanoparticle Assemblies.

DNA origami mechanisms offer promising tools for precision nanomanipulation of molecules or nanomaterials. Recent advances have extended the function of individual DNA origami devices to material scales via hierarchical assemblies. However, achieving rapid and precise control of large conformational changes in hierarchical assemblies remains a critical challenge. Here, we demonstrate a method for controlling DNA origami-nanoparticle assemblies through a multiscale approach, in which nanoparticles impart control on the conformation of individual DNA origami mechanisms, whereas DNA origami assemblies control the conformation of nanoparticle arrays. Specifically, we show that the angular distributions of DNA origami hinge mechanisms are tunable as a function of nanoparticle size and distance from the hinge vertex. We selectively adjust the affinity of nanoparticle binding sites, resulting in hinge actuation via DNA melting without releasing the nanoparticle, thereby enabling rapid and reversible temperature-based actuation. Finally, we demonstrate this rapid actuation in DNA origami-nanoparticle arrays of length scales extending over a micron. These results provide guiding principles toward the design of dynamic, DNA-origami hierarchical materials capable of storing and releasing mechanical energy.

Dynamic Control of DNA Origami Nanostructures via Gold Nanoparticles

A major direction of research in DNA origami nanotechnology is the folding of DNA into complex 3D shapes with the inclusion of flexible regions to form dynamic nanostructures. These types of dynamic nanostructures are typically actuated via the addition DNA “fuel” strands that form new connections to reconfigure a structure, or via the selective removal of DNA components via strand displacement. The goal of this work is to enable novel actuation methods with distinct, and potentially faster, triggering mechanisms based on incorporating other nanomaterial components. While DNA origami has been used in combination with other nanomaterials such as gold nanoparticles there has yet to be a demonstration of nanoparticles used for the precise control of nanostructure actuation. Using a DNA origami hinge mechanism we have included single-stranded DNA overhangs extending from the arms, which bind to a gold nanoparticle to latch the hinge closed. By varying where the nanoparticle is incorporated (distance from the hinge vertex) and the nanoparticle size we have shown that the angular distributions of the hinge are highly controllable. In addition, tuning the nanoparticle binding affinity of the bottom arm relative to the top arm allows for actuation of the hinge via DNA melting without releasing the nanoparticle entirely, thereby enabling reversible temperature-based actuation. Particle binding and hinge actuation were monitored via a two color fluorescence quenching setup to reveal that the kinetics of actuation occur on the minute timescale. Future work will explore light-based actuation mediated by local plasmonic heating of the nanoparticles. We have also polymerized hinges into dynamic assemblies, which in combination with nanoparticle based actuation schemes will establish a basis for rapidly reconfigurable materials with future applications in biosensing, plasmonics, and bioenergetics.

Algorithm for Identifying the Maximum Detour Hinge Vertices of a Permutation Graph

Algorithm for Identifying the Maximum Detour Hinge Vertices of a Permutation Graph

Algorithm for Finding Maximum Detour Hinge Vertices of Interval Graphs

Consider a simple undirected graph G = (V,E) with vertex set V and edge set E. Let G-u be a subgraph induced by the vertex set V-{u}. The distance δG(x,y) is defined as the length of the shortest path between vertices x and y in G. The vertex u ∈ V is a hinge vertex if there exist two vertices x,y ∈ V-{u} such that δG-u(x,y)>δG(x,y). Let U be a set consisting of all hinge vertices of G. The neighborhood of u is the set of all vertices adjacent to u and is denoted by N(u). We define d(u) = max{δG-u(x,y) | δG-u(x,y)>δG(x,y),x,y ∈ N(u)} for u ∈ U as detour degree of u. A maximum detour hinge vertex problem is to find a hinge vertex u with maximum d(u) in G. In this paper, we proposed an algorithm to find the maximum detour hinge vertex on an interval graph that runs in O(n2) time, where n is the number of vertices in the graph.

Erratum and addendum to “A linear time algorithm for finding all hinge vertices of a permutation graph” [Information Processing Letters 59 (2) (1996) 103–107

This note points out and corrects an error in the algorithm proposed in [Ting-Yem Ho, Yue-Li Wang and Ming-Tsan Juan, A linear time algorithm for finding all hinge vertices of a permutation graph, Information Processing Letters 59 (2) (1996) 103–107].

An Optimal Parallel Algorithm for Finding All Hinge Vertices of a Circular-Arc Graph

Let G = (V, E) be an undirected simple graph with u e V. If there exist any two vertices in G whose distance becomes longer when a vertex u is removed, then u is defined as a hinge vertex. Finding the set of hinge vertices in a graph is useful for identifying critical nodes in an actual network. A number of studies concerning hinge vertices have been made in recent years. In a number of graph problems, it is known that more efficient sequential or parallel algorithms can be developed by restricting classes of graphs. In this paper, we shall propose a parallel algorithm which runs in O(log n) time with O(n/log n) processors on EREW PRAM for finding all hinge vertices of a circular-arc graph.

An efficient distributed algorithm for finding all hinge vertices in networks

Let G=(V, E) be a graph with vertex set V of size n and edge set E of size m. A vertex v∈V is called a hinge vertex if there exist two vertices in V\\{v} such that their distance becomes longer when v is removed. In this paper, we present a distributed algorithm that finds all hinge vertices on an arbitrary graph. The proposed algorithm works for named static asynchronous networks and achieves O(n 2) time complexity and O(m) message complexity. In particular, the total messages exchanged during the algorithm are at most 2m(log n+nlog n+1) bits.

An Efficient Algorithm for Finding All Hinge Vertices on Trapezoid Graphs

The distance between at least two vertices becomes longer after the removal of a hinge vertex. Thus a faulty hinge vertex will increase the overall communication cost in a network. Therefore, finding the set of all hinge vertices in a graph can be used to identify critical nodes in a real network. An O(n log n) time algorithm has been proposed here to find all hinge vertices of a trapezoid graph with n vertices.

The optimal sequential and parallel algorithms to compute all hinge vertices on interval graphs

If the distance between two vertices becomes longer after the removal of a vertexu, thenu is called a hinge vertex. In this paper, a linear time sequential algorithm is presented to find all hinge vertices of an interval graph. Also, a parallel algorithm is presented which takesO(n/P + logn) time usingP processors on an EREW PRAM.

The recognition of geodetically connected graphs

Let G = ( V, E) be a graph with vertex set V of size n and edge set E of size m. A vertex υ ϵ V is called a hinge vertex if the distance of any two vertices becomes longer after v is removed. A graph without hinge vertex is called a hinge-free graph. In general, a graph G is k-geodetically connected or k-GC for short if G can tolerate any k − 1 vertices failures without increasing the distance among all the remaining vertices. In this paper, we show that recognizing a graph G to be k-GC for the largest value of k can be solved in O( nm) time. In addition, more efficient algorithms for recognizing the k-GC property on some special graphs are presented. These include the O( n + m) time algorithms on strongly chordal graphs (if a strong elimination ordering is given), ptolemaic graphs, and interval graphs, and an O( n 2) time algorithm on undirected path graphs (if a characteristic tree model is given). Moreover, we show that if the input graph G is not hinge-free then finding all hinge vertices of G can be solved in the same time complexity on the above classes of graphs.

Finding the set of all hinge vertices for strongly chordal graphs in linear time

Let V( G) be the vertex set of a graph G = ( V,E), and let G — u be the subgraph induced by the vertex set V( G) - { u}. A vertex u ε V( G) is said to be a hinge vertex of G if and only if there exist two vertices x, y ε V( G-u) such that d G — u ( x,y) > d G ( x,y), where d G ( x, y) is the distance (the length of a shortest path) between x and y in G. In this paper, based on the breadth-first search technique, an O( n+ e) time algorithm is proposed for finding the set of all hinge vertices of a strongly chordal graph when a strong elimination ordering is given.

A linear time algorithm for finding all hinge vertices of a permutation graph

If the distance of any two vertices becomes longer after a vertex u is removed, then u is called a hinge vertex. The fault of a hinge vertex will increase the overall communication cost in a network. Therefore, finding the set of all hinge vertices in a graph can be used to identify critical nodes in a real network. We shall propose a linear time algorithm for finding all hinge vertices of a permutation graph.